Limit analysis of 3D masonry block structures with non-associative frictional joints using cone programming

• A new three-dimensional limit analysis model for masonry structures is presented.
• Non-associative friction is modelled by iterative solution of a SOCP problem.
• Good agreement with existing numerical benchmarks is observed.
• Masonry walls and a building tested experimentally are successfully modelled.
• Solutions are obtained much more rapidly than when using existing methods.

A three-dimensional limit analysis model for masonry structures is presented. In the model the masonry is discretized as an assemblage of rigid blocks, which interact via no-tension contact surfaces with Coulomb friction. A concave contact formulation is adopted and an iterative solution procedure is used to allow the underlying non-associative friction problem to be solved. Second order cone programming (SOCP) is used to allow direct modelling of the conic failure surface. The formulation is validated against various numerical benchmark problems and then successfully applied to masonry walls and a small-scale masonry building tested experimentally.